Ikeme let a back-pass from David Davis go through his legs in their Championship relegation scrap with Bristol City on Saturday.
Dean Saunders' side came from behind to win the game 2-1 but Ikeme is understood to be angry at being the subject of criticism from his manager at half-time for his part in the own goal.
The 26-year-old punched a tactics board in the dressing room which may have led to him breaking a bone in his hand, with Dorus de Vries subsequently coming on in his place for the second half at Molineux.
Saunders, who originally denied the incident took place, said: "After the game I didn't know he had broken his hand.
"I wanted to protect Carl and protect what goes on inside the dressing room but now it has all come out I have a responsibility to let the supporters know why he's not available to play.
"Carl was frustrated at making his mistake and has punched the tactics board which is only cardboard but there is a metal bar at the back of it which has damaged his hand.
"I'm not sure whether he will be out for the season but it will be for some weeks."
Saunders has recalled Republic of Ireland U21 international Aaron McCarey from his loan spell at Walsall to offer cover to De Vries.